Age versus Size of the Universe

[Johninch]

I have learned a lot about cosmology on this forum, but I’m still behind on the logic.

So far I have understood that, since the universe is everything, it cannot have a center nor a boundary. But it does have an expansion and that’s when my problems start.

I would like to concentrate on a couple of questions, in order to make some progress:

- if we know the age of the universe and we know its rate of expansion, why is there so much discussion about its total size?
- if the size of the universe is finite, how can the universe be isotropic?
- assuming that the universe is flat and finite, how can it not have a boundary?

I am not talking about the observable universe, I am talking about the total universe. Further, I am assuming that BBT refers to the total universe.

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[Johninch]

Thanks, it's a good revision, but it doesn't answer my questions.

It does however mention that the consensus is that the universe is nearly flat and therefore extremely large, although not infinite.

I would have quite a problem with BBT if it were suggested that the universe is infinitely large, but even if we just stick with the assumption that it is extremely large, this emphasizes one of my problems.

If we increase our estimate of the size of the universe to near infinite proportions and we have a fixed idea of the rate of expansion (including variations over time so far), what happens to our estimate of the age of the universe? Does that approach infinity too?

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[phinds]

Does the surface of the Earth have an edge?

The universe can be finite but unbounded, like the surface of the Earth.

 

[marcus]

I see Phinds beat me to it

...
- if we know the age of the universe and we know its rate of expansion, why is there so much discussion about its total size?
- if the size of the universe is finite, how can the universe be isotropic?
- assuming that the universe is flat and finite, how can it not have a boundary?
.

Second question: For the 2D creatures living on the surface of a sphere, the sphere surface (their space) is isotropic.

Third question: Think of a "Pac Man" flat 2D universe which is a square with opposite edges identified. So if a feature slides off the right edge he reappears coming in on left. Likewise top and bottom. Topologically it is a torus, the 2D surface of a donut. But there is no curvature. This universe is not embedded in any higher dimensional space. It is an edgeless flat square which has been made edgeless by identifying or "gluing" opposite sides.

These 2D sketches have 3D analogs which are not too hard to imagine living in. Don't try to picture them from the "outside" because there is no outside where you could stand and look at them. The way to conceptualize is to imagine the experience of living in such a space and moving around in it. Stretching string, light rays, circumnavigating etc.

First question: We know the expansion rate as a PERCENTAGE PER UNIT TIME and we can estimate the past history of this percentage rate.
That does not tell us the overall absolute size.
You are very welcome to ask more questions about this. If it isn't clear why knowing percentage expansion rate history does not tell absolute size, keep on asking. I don't want to make this post longer because it may not be necessary.

The present Hubble constant is equivalent to saying that distances increase by 1/139 of one percent every million years. It tells us what individual distances do. It does not tell the overall absolute size.

The classic model does not include a model of the universe at the precise start of expansion so there is no "size" to start with. Some newer models (like Loop quantum cosmology) DO include the start of expansion and may have a finite size (at for example the time of the bounce---there is a bounce instead of a mathematical failure). But so far the overall size at start of expansion has not been determined in the new, singularity-free models. So we only know percentage growth and we cannot pinpoint initial size.

However it might eventually turn out to be possible to estimate PRESENT size and then extrapolate back.

 

[phinds]

I see Phinds beat me to it

Yes, but as always, you present a MUCH more complete and coherent discussion.

 

[Johninch]

Marcus beat me too, while I was composing this answer to Phinds. I will study Marcus' reply afterwards.

Does the surface of the Earth have an edge?

The universe can be finite but unbounded, like the surface of the Earth.

No, the surface of the Earth does not have an edge and the universe is also not like the two dimensional surface of the earth, so it's irrelevant.

Are you saying that the universe is closed? If so, the universe has the shape of a sphere and will have a boundary. Otherwise, what does closed mean?

The consensus is that the universe is flat or nearly flat. If it's flat, it will not have an edge or boundary, but the problem for me is that it would be infinitely large, according to the generally accepted model of a flat universe.

If it's nearly flat, it will be huge and presumably this is the reason for the discussion about it's size, because nobody can say how huge it is. My question is, if we debate the size of the universe, do we have to adjust the age of the universe in order to get to the speculated size, or do we have to adjust the rate of expansion, or what?

I would also like to know, what do the inhabitants of the oldest galaxy see. Does the universe look isotropic from there? This relates to the boundary question.

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[Johninch]

We know the expansion rate as a PERCENTAGE PER UNIT TIME and we can estimate the past history of this percentage rate.
That does not tell us the overall absolute size.
You are very welcome to ask more questions about this. If it isn't clear why knowing percentage expansion rate history does not tell absolute size, keep on asking. I don't want to make this post longer because it may not be necessary.

The present Hubble constant is equivalent to saying that distances increase by 1/139 of one percent every million years. It tells us what individual distances do. It does not tell the overall absolute size.

The classic model does not include a model of the universe at the precise start of expansion so there is no "size" to start with. Some newer models (like Loop quantum cosmology) DO include the start of expansion and may have a finite size (at for example the time of the bounce---there is a bounce instead of a mathematical failure). But so far the overall size at start of expansion has not been determined in the new, singularity-free models. So we only know percentage growth and we cannot pinpoint initial size.

However it might eventually turn out to be possible to estimate PRESENT size and then extrapolate back.

My further questions about boundary are contained in my posting to Phinds.

Concerning size and age: I can see the problem of not having the starting size, but we do have the diameter of the observable universe (93 mly) and the current rate of expansion (70 km/sec/Mps) and estimates of the lower rates of expansion in the past. So logically we should be able to extrapolate back to a smaller size near to the BB.

Then we have various data from WMAP etc, plus other observations from astronomy, so altogether we can come up with a history of the universe including BBT. Ok, that's all we can do in the observable universe.

What we don't have, are reliable estimates about the size of the unobservable universe. I have seen some extremely big figures, which would tie into the concept of a nearly flat universe. What bothers me is, having done our observations and calculations for BBT, how do we square our age of the universe and expansion rates with the size of the total universe.

The unobservable universe also came from the BB didn't it? I mean, the larger the universe, the older or faster expanding it is. So just how reliable is the figure of 13.7 bn?

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[phinds]

... assuming that the universe is flat and finite, how can it not have a boundary?

THIS is that statement that lead me to attempt to help you understand that it is NOT necessary that if something is finite it has a boundary. The surface of the Earth is finite and yet does not have a boundary. Do you dispute this? By analogy the total universe also can be finite and yet unbounded.

The univerese is NOT, as far as we know, shaped like a sphere, but WHATEVER the shape, it does not have to be bounded (or unbounded for that matter --- it has to be one or the other but we don't know which).

 

[Naty1]

What bothers me is, having done our observations and calculations for BBT, how do we square our age of the universe and expansion rates with the size of the total universe.

We don't. Nobody knows the size of the universe. On the surface of the earth, you might be able to make a guess about the total size of the Earth based on the horizon distance, curvature, etc. But for the universe you can't even make such an estimate based on any existing observations or theory.

Maybe a crude analogy would be trying to figure out how far a distant object is from you on Earth a foggy day, dead of night [no light signals whatsoever, no radar reflection,etc] while it's drifting away...you can't see it nor detect it in any way. The cosmological 'fog' is the origin of relic radiation, called the surface of last scattering.

For calculations on what we do know, see Marcus' discussion here:

https://www.physicsforums.com/showthread.php?t=634757&page=3

So just how reliable is the figure of 13.7 bn?

New satellite based observations now suggest it is about 13.4 by old.
In future years we'll probably have newer observational data.

 

[Johninch]

The surface of the Earth is finite and yet does not have a boundary. Do you dispute this? By analogy the total universe also can be finite and yet unbounded.

The univerese is NOT, as far as we know, shaped like a sphere, but WHATEVER the shape, it does not have to be bounded (or unbounded for that matter --- it has to be one or the other but we don't know which).

I already replied that I agree, the surface of the Earth does not have a boundary. So what? We are living in 3d space, so your analogy is meaningless.

I already told you that the universe is not shaped like a sphere. It's flat or nearly flat.

What is the basis for your statement that it does not have to be bounded? You say it has to be one or the other but we don't know which. You seem to be suggesting that I am wrong to assume a boundary. Why? I am only saying that finite things usually have a boundary, so the universe may have one too. What's wrong with that?

I am aware that everybody assumes that the universe has no boundary, but the whole point of my questions is to understand the logic of these matters.

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[Whovian]

I already replied that I agree, the surface of the Earth does not have a boundary. So what? We are living in 3d space, so your analogy is meaningless.

The analogy can be extended to a 3-dimensional "surface."

I already told you that the universe is not shaped like a sphere. It's flat or nearly flat.

Nearly flat doesn't mean "not shaped like a sphere," and there are plenty of other models, such as a 3-torus-like Universe. The 3-sphere is an example.

What is the basis for your statement that it does not have to be bounded? You say it has to be one or the other but we don't know which. You seem to be suggesting that I am wrong to assume a boundary. Why? I am only saying that finite things usually have a boundary, so the universe may have one too. What's wrong with that?

What happens when you cross that boundary? It should be theoretically possible, and once you do, you're ... umm ... outside the Universe. And the Universe, by definition, is everything, and thus being outside the Universe is impossible. (Again, by definition.)

 

[marcus]

The analogy can be extended to a 3-dimensional "surface."
Nearly flat doesn't mean "not shaped like a sphere," and there are plenty of other models, such as a 3-torus-like Universe. The 3-sphere is an example.
What happens when you cross that boundary? It should be theoretically possible, and once you do, you're ... umm ... outside the Universe. And the Universe, by definition, is everything, and thus being outside the Universe is impossible. (Again, by definition.)

Whovian and Phinds, great answers! I hope the questioner's curiosity is eventually satisfied.
It's important for people to realize that what is meant by "nearly flat" could in fact be "3-spherical but very large". A very large spherical surface would seem nearly flat to creatures living in it. Near flatness, in that case, just translates into the 3-sphere having a very large radius of curvature.

And a nice thing is that the radius of curvature can be estimated from today's observational data. Alternatively, bounds on the CIRCUMFERENCE of the 3-sphere can be estimated. That is just 2 pi times the radius of curvature. It is how long you would have to travel in a straight line before you get back to your point of departure.

The calculation, in case some readers haven't seen it before, is very simple. You take the Hubble distance (often given as 13.9 billion ly, or 14 billion for round numbers) and multiply by 2 pi. That gives around 88 billion ly. Then you divide that by the square root of minus the Ω_k number that is derived from all the combined data from CMB observations, supernovae, galaxy counts etc.

the estimate of Ω_k keeps getting better as more data is collected. A good recent source is Hinshaw et al, which was just revised as of 30 January. Just google "Hinshaw nine-year"
These are the final results of the 9 year WMAP project. The report is called "WMAP9" for short.
For instance look at their Table 10, on page 20, where they give 95% confidence intervals which depend on which data sets they combined to get the result.
Combining all the data sets (WMAP+eCMB+BAO+H₀ +SNe) gives the results in the rightmost column.
The confidence interval for - Ω_k is [0.0025, 0.0105]

Let's take the smallest thing to divide 88 billion ly by, that will give the largest circumference. The square root of 0.0025 is 0.05. So divide 88/0.05 = 1760 billion ly.

This works as long as the estimate of Ω_k is negative, so when you take minus you get a positive number, and the square root makes sense.

So according to that confidence interval, from Table 10, the largest the circumference could be is 1760 billion ly.
Now what is the SMALLEST it could be? Well the square root of 0.0105 is about 0.1 and dividing by that is like multiplying by 10, so the smallest the circumference could be is around 880 billion ly.

The main thing is we have no evidence for there being "space outside of space" or for there being any boundary to space. So it could be infinite, or it could be something like a 3-sphere. These are the simplest things to imagine and the model builders are normally aiming for the simplest model with the best fit to the data.
Googling "Hinshaw nine-year" gets you http://arxiv.org/abs/1212.5226
the dataset abbreviations are explained on page 2.
eCMB means "external CMB dataset" from other than WMAP itself, i.e. South Pole Telescope (SPT) and Atacama Cosmology Telescope (ACT). Of course SNe means supernovae data. BAO (baryon acoustic oscillation) basically means counting galaxies at different distances to detect "ripples" in the average bulk matter of the universe.

 

[Johninch]

What happens when you cross that boundary? It should be theoretically possible, and once you do, you're ... umm ... outside the Universe. And the Universe, by definition, is everything, and thus being outside the Universe is impossible. (Again, by definition.)

No, I think it is not theoretically possible. If the universe is everything, you can't go outside it. If the universe is expanding at greater than the speed of light in the outer regions, so would be the boundary.

The boundary would be where an observer could (perhaps) see galaxies on one side of the sky but definitely not on the other side because there are none. Can you give me a reason why this is not possible?

I am not making up stories, I am just trying to make sure that it is illogical to think of a boundary.

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[Chronos]

The observable universe definitely has a 'boundary' of sorts. It is called the particle horizon, which, simply put, is merely the age of the universe multiplied by the speed of light. We do, however, have solid reasons to believe the entirety of the universe is far larger than the little patch within our particle horizon. It could even be infinite, although the only thing we can deduce with any degree of reliability is a minimum size. It is worth noting that the particle horizon is not a boundary in any conventional sense. Objects in the universe may freely pass beyond our particle horizon without 'leaving' the universe. They merely become unobservable. Every observer in the universe is 'special' in this sense, they all have their very own personal particle horizon that is unique to their location.

 

[marcus]

No, I think it is not theoretically possible. If the universe is everything, you can't go outside it. If the universe is expanding at greater than the speed of light in the outer regions, so would be the boundary.

The boundary would be where an observer could (perhaps) see galaxies on one side of the sky but definitely not on the other side because there are none. Can you give me a reason why this is not possible?

I am not making up stories, I am just trying to make sure that it is illogical to think of a boundary.

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You understand do you not, that space can expand without haveing any other space outside it to expand into.

The universe is usually considered to be all space and the space is what is expanding so you are not imagining a boundary of the universe, but a boundary to the part occupied by matter. I see nothing wrong with imagining that. Why not?

But it makes things mathematically very complicated and there is no evidence that matter is like that: confined to some limited part of the universe.

The simplest mathematical picture is that however much space there is, it is uniformly filled with matter---over large scale average density is approximately even.
There is no evidence this is NOT true so there is no reason to unnecessarily complicate things by imagine matter in only one part of the universe.

They are always going for the simplest best-fit model. The simplest that gives the best fit.

Of course cosmologists are always looking for evidence that would challenge their consensus model. One of the things they are always sounding the alarm about is someone thinks he has seen some evidence of largescale NON-uniformity. Statistically fewer galaxies in some direction, or something. So far I've seen a bunch and they always turned out to be "false alarms" and were eventually ignored or abandoned.

Some inflation scenarios give rise to bubbles in the midst of a vast irregular universe in which expansion is occurring at different rates, so that would represent a kind of non-uniformity. But one does not actually USE such models to fit observational data to. They are more in the realm of speculation
================
One reason large scale uniformity is the simplest assumption is that in GR, which is the well tested prevailing law both of gravity and geometry, matter and geometry interact on an intimate basis. They shape and guide each other. It is natural to think of matter and geometry as co-extensive. Would make the math a lot harder to have matter confined to only one part of an expanding universe. And after all, why should it be?

 

[Johninch]

You understand do you not, that space can expand without haveing any other space outside it to expand into.

The universe is usually considered to be all space and the space is what is expanding so you are not imagining a boundary of the universe, but a boundary to the part occupied by matter. I see nothing wrong with imagining that. Why not?

But it makes things mathematically very complicated and there is no evidence that matter is like that: confined to some limited part of the universe.

The simplest mathematical picture is that however much space there is, it is uniformly filled with matter---over large scale average density is approximately even.
There is no evidence this is NOT true so there is no reason to unnecessarily complicate things by imagine matter in only one part of the universe.

I consider that the universe is everything which exists. The universe includes all baryonic matter, dark matter, dark energy, dirac space and anti-matter. There is nothing beyond the universe because nothing does not exist.

I have no problem with the assumption that matter is uniformly distributed within the observable universe. If we assume that the total universe is several orders of magnitude larger than this, then a locally uniform distribution of matter would seem to be a reasonably likely local phenomenon. However, it seems speculative to assume that this local density and uniformity is repeated over the whole universe.

I interpret your remarks concerning the irregularities in the CMBR as meaning that although we interpret those irregularities to result in the formation of matter and galaxies, we nevertheless assume that the expansion of the universe has always proceeded at an equal rate for all galaxies everywhere. This would give us the even distribution. Please check: I previously understood that some galaxies are receding much faster than others, which would give the universe a non-uniform distribution and a non-spherical shape. But now I understand that the difference in the calculated speed of distant galaxies is only (mainly) due to distance and time, right?

You apparently misinterpreted my post concerning the boundary. I was referring to the boundary of the universe and not the boundary of the part occupied by matter, baryonic or otherwise. That is to say, outside my imagined boundary there is not anything. The imagined situation is the following:

I am magically and immediately transferred from here to a planet on the edge of a galaxy where I can only see the local milky way plus other galaxies on one side of the sky only. All of those galaxies appear to be receding at a very fast and accelerating rate. On the other side of the sky I do not see anything at all. It is totally dark to my eyes and to all of my very advanced instruments. I fully understand BBT. What do I conclude?

Here are my answers:
-My planet is on that boundary of the galaxy farthest from the rest of the universe.
-My galaxy is at a boundary of the universe, beyond which there is no more universe.
-As I do not observe anything in the “dark” direction, I have to assume that there is absolutely nothing there.
-To make sure, I send a rocket up. It performs “normally” but the onboard instruments do not detect anything (except itself).

What’s wrong with that? Is there a reason why the imagined planet cannot logically exist?

.

 

[Johninch]

We do, however, have solid reasons to believe the entirety of the universe is far larger than the little patch within our particle horizon. It could even be infinite.

Thanks for your clear summary Chronos. The only piece which I object to is the reference to infinity.
I don't want to start a philosophical discussion, I only want you to know that I noticed it!

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[Naty1]

Marcus:

I have no problem with the assumption that matter is uniformly distributed within the observable universe. ... However, it seems speculative to assume that this local density and uniformity is repeated over the whole universe.

I am not so sure as Marcus about the last sentence...the 'speculative' part... I note that each day we receive new cosmic background radiation,CMBR, from which at the time of its origin the early seeds of the universe were present, and those signals appear with the same characteristics as yesterday's, and the day before and the day before that and...so forth. So from what Marcus has taught me I conclude as the observable universe grows each day, it exhibits the same radiation characteristics as the prior day and that at least suggests that there is nothing unusual just beyond yesterday's observations. So I expect tomorrows CMBR
will be just like todays.

Chronos:

It could even be infinite.

Another way to express this, I think, is that an infinite universe cannot so far be ruled out.

 

[timmdeeg]

The consensus is that the universe is flat or nearly flat. If it's flat, it will not have an edge or boundary, but the problem for me is that it would be infinitely large, according to the generally accepted model of a flat universe.

If it's nearly flat, it will be huge and presumably this is the reason for the discussion about it's size, because nobody can say how huge it is. .

Let's assume that the universe is exactly flat and obeys the FRW model. Flat then means locally flat because nothing else we are able to measure. However the model says that an arbitrary oberver will agree to that regarding his local position in the universe. Thus globally viewed the curvature is constant, well in accordance with the cosmological principle one of the consequences of which is that there is no center and no boundary.

Still, even being exactly flat leaves the global structure of the universe, it's topology, open. In case the universe has a compact topology, e.g. a 3-torus which is flat locally, then it's size is finite. Some date indicate this possibility.

If it's nearly flat, we know less.

 

[marcus]

Hi John, I'm more of a cosmology-watcher than a participant. I follow developments as best I can, and love the subject. This is my personal perspective. To answer the part I highlighted in blue I would say that cosmology is a mathematical science i.e. it aims at the simplest best-fit mathematical model. And GR is our law of gravity and our law of geometry (why triangles add up to approximately but not exactly 180 and how matter affects this) that we base the cosmic model on.

Someday GR will be improved but for now it is the accepted dynamics of geometry that has been tested repeatedly in many ways and passed all the tests and has proven remarkably accurate.

So the key thing to realize is that cosmology is an APPLICATION of the accepted law of gravity/geometry. The aim is not merely an ad hoc model that fits the observational data- it is to find the simplest bestfit model which is a solution of the GR equation.
The simplest best-fit model which accords with the currently accepted dynamics of geometry and matter.

I consider that the universe is everything which exists. The universe includes all baryonic matter, dark matter, dark energy, dirac space and anti-matter. There is nothing beyond the universe because nothing does not exist.

I have no problem with the assumption that matter is uniformly distributed within the observable universe. If we assume that the total universe is several orders of magnitude larger than this, then a locally uniform distribution of matter would seem to be a reasonably likely local phenomenon. However, it seems speculative to assume that this local density and uniformity is repeated over the whole universe.

I interpret your remarks concerning the irregularities in the CMBR as meaning that although we interpret those irregularities to result in the formation of matter and galaxies, we nevertheless assume that the expansion of the universe has always proceeded at an equal rate for all galaxies everywhere. This would give us the even distribution. Please check: I previously understood that some galaxies are receding much faster than others, which would give the universe a non-uniform distribution and a non-spherical shape. But now I understand that the difference in the calculated speed of distant galaxies is only (mainly) due to distance and time, right?

You apparently misinterpreted my post concerning the boundary. I was referring to the boundary of the universe and not the boundary of the part occupied by matter, baryonic or otherwise. That is to say, outside my imagined boundary there is not anything. The imagined situation is the following:

I am magically and immediately transferred from here to a planet on the edge of a galaxy where I can only see the local milky way plus other galaxies on one side of the sky only. All of those galaxies appear to be receding at a very fast and accelerating rate. On the other side of the sky I do not see anything at all. It is totally dark to my eyes and to all of my very advanced instruments. I fully understand BBT. What do I conclude?

Here are my answers:
-My planet is on that boundary of the galaxy farthest from the rest of the universe.
-My galaxy is at a boundary of the universe, beyond which there is no more universe.
-As I do not observe anything in the “dark” direction, I have to assume that there is absolutely nothing there.
-To make sure, I send a rocket up. It performs “normally” but the onboard instruments do not detect anything (except itself).

What’s wrong with that? Is there a reason why the imagined planet cannot logically exist?

.

I suppose that LOGICALLY you can send a rocket probe into non-existence and you can imagine a region of nothingness and a region of existence and a boundary between them. I can't think of a LOGICAL reason not to imagine a rocket going thru the boundary and its onboard sensors not detecting anything except its own existence.

But I don't think that one can MODEL that situation with a SOLUTION OF THE GR equation. A region of non-existence is not a feature of our currently accepted dynamics of geometry and matter, which we are pretty much stuck on using as the best available so far.

Now to respond to the blue highlight paragraph. I think the assumption of approximate uniformity is a reasonable working assumption because
1) it is simple
2) so far no evidence to the contrary has withstood scrutiny

People regularly review this assumption to see how it is holding up, and people challenge it now and then. It is a serviceable working assumption, I would not think of it as an article of faith. As long as the model continues to fit the data people will keep on using it---until something better shows up.

 

[marcus]

Hi Naty, in post #18 it sounded as if you were quoting me but I think you were actually quoting John, so i was a bit confused and didn't see how to respond.

 

[Johninch]

I suppose that LOGICALLY you can send a rocket probe into non-existence and you can imagine a region of nothingness and a region of existence and a boundary between them. I can't think of a LOGICAL reason not to imagine a rocket going thru the boundary and its onboard sensors not detecting anything except its own existence.

Thank you Marcus for your patient comments.

However, in the part of your reply quoted above, you are being too generous towards my logic!

My thought experiment of sending a rocket in the opposite direction to all of the known universe does not involve going through a boundary into nothingness. That's impossible. The rocket is part of the universe and is enlarging it.

This is my way of illustrating how the universe could have a boundary. The universe does not need any space to expand into, it creates its own space by expanding. This is what you told me already, so I am sure you agree.

With my thought experiment I am merely wanting to show that it's possible to be at the boundary of the universe without implying that there is anything beyond. So far I have read everywhere that the universe does not have a boundary. So if my experiment is possible, then it can have a boundary.

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[Naty1]

Marcus:

Hi Naty, in post #18 it sounded as if you were quoting me but I think you were actually quoting John...,

from #18:

So from what Marcus has taught me I conclude as the observable universe grows each day, it exhibits the same radiation characteristics as the prior day...

DUDE! I was throwing you a COMPLIMENT... from several years of prior discussions.
Relax and enjoy; Bask in the glory! [LOL]

 

[marcus]

Thanks for the compliment, Naty! What puzzled me in your post #18 was that it looked like you were quoting me, saying "it seems speculative" when the words in quotes were actually from somebody else. I knew I had not said what you had me down as saying, so I went back looking for those words and found they were from Johninch.

Marcus:

I have no problem with the assumption that matter is uniformly distributed within the observable universe. If we assume that the total universe is several orders of magnitude larger than this, then a locally uniform distribution of matter would seem to be a reasonably likely local phenomenon. However, it seems speculative to assume that this local density and uniformity is repeated over the whole universe...

I am not so sure as Marcus about the last sentence...the 'speculative' part... I note that each day we receive new cosmic background radiation,...
... So I expect tomorrows CMBR will be just like todays.

Chronos:

[actual quote from Chronos]

Another way to express this, I think, is that an infinite universe cannot so far be ruled out.

You give a cogent reason for not regarding the cosmological assumption of uniformity as all that speculative. I guess now that I think of it the only problem was your post should have begun:
=======
Johninch:

...

I am not so sure as Johninch about the last sentence...
=======

What you were saying made a lot of sense, you just had the people's names confused. I see now how I should have responded.

 

[marcus]

I wouldn't call the cosmological principle (the basic uniformity assumption) speculation, exactly. It think it comes under the heading of Occam's Razor---the idea is that in a mathematical science you should use the SIMPLEST model that fits.

You keep the model simple until you actually get evidence that you need to make it more complicated. And you keep watching out for such evidence!

I would call it speculative to start imagining some boundary off somewhere too far away for us to see, when we have no indication of a boundary. Some day we might, but we haven't yet seen any suggestion of one that withstood scrutiny.

I would likewise call it speculative to start assuming there is a center of the universe far away in some direction (but we just don't know in what direction to point in :-)

Those would be unnecessary complications for which there is no justification. But we should always keep an eye out for any asymmetries in the statistics that might suggest NON-uniformity. And people do watch for that, and periodically sound the alert. What I've seen happen is that the alleged evidence is carefully examined---and so far has been found wanting, and dismissed.

 

[Naty1]

Marcus

Thanks for the compliment, Naty! What puzzled me in your post #18 was that it looked like you were quoting me, saying "it seems speculative" when the words in quotes were actually from somebody else.

Listen up: At my age I'm increasingly likely to misquote, and if I do happen to get a quote correct, to mis-attribute the source. get used to it!

Just be glad I threw the compliment at the correct person!

 

[Johninch]

Thanks everybody for your help on my questions. In the meantime I have been reading more about the cosmological principle, which doesn’t allow a boundary to the universe. Therefore my example of half the sky not containing anything is simply false. Why this cosmological principle has to be true, I don’t understand yet, but I accept it as current theory.

To conclude, could somebody give me definitive answers to the following questions (please note that I am talking about the total universe and not just the observable universe):

1) Does the cosmological principle imply that the universe is infinite? This seems to follow from it not having any boundary. Why then do I read about the universe having dimensions like radius and a certain number of galaxies outside of the observable portion?

2) How do I get from the finite BB event to an infinite universe? How can the universe expand when it is already infinite and boundless? I already know that expansion means distances increasing. Perhaps it has to be explained to me what infinite means.

Please note too, that a) I never suggested that the universe had or has a center, b) I never suggested that my imagined boundary could be crossed and c) I always understood that the universe could double back on itself, so that there would be no boundary in certain directions.

I am really not wanting to challenge the cosmological principle, I just want to understand what current theory is saying.

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[Naty1]

1) Does the cosmological principle imply that the universe is infinite?

No. We discuss various sizes regardless of how big the cosmos might be overall; just as you can discuss distances in your local home neighborhood without knowing the size of the earth.

Best bet is to read here about the cosmological principle:

http://en.wikipedia.org/wiki/Cosmological_principle

2) How do I get from the finite BB event to an infinite universe?

The big bang has no defined size nor does the universe.

This might be a good time to reread the posts above as Chronos,for one, already answered the question about the 'size of the universe':

...We do, however, have solid reasons to believe the entirety of the universe is far larger than the little patch within our particle horizon. It could even be infinite, although the only thing we can deduce with any degree of reliability is a minimum size...

edit: I see I also answered it already: " Nobody knows the size of the universe..." and so have others...
It does take a while to absorb such information and to then try to put the pieces together...

 

[Johninch]

My question: Does the cosmological principle imply that the universe is infinite?
Your answer:

No. We discuss various sizes regardless of how big the cosmos might be overall

Wiki clearly states: "The cosmological principle implies that at a sufficiently large scale, the universe is homogeneous; different places will appear similar to one another."

Well then, in whichever direction and however far I travel, I will see more of the same. What’s the difference between that and infinity?



My question: How do I get from the finite BB event to an infinite universe?
Your answer:

The big bang has no defined size nor does the universe.

I am not asking for the size of the BB nor of the universe, I just want to know, as a first step, whether we are saying that the universe is finite or infinite.

It does take a while to absorb such information and to then try to put the pieces together...

Yes, well, it’s certainly difficult for me.


Basically we are stuck on the point, whether BBT is compatible with an infinite universe. My reading is that it is not.

If I am right that the universe must be finite, I want to understand why it is not possible to stand somewhere and look in some direction and see few or no galaxies. We don’t have to call it a boundary or edge if that jars.

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[Naty1]

"The cosmological principle implies that at a sufficiently large scale, the universe is homogeneous; different places will appear similar to one another."

Well then, in whichever direction and however far I travel, I will see more of the same. What’s the difference between that and infinity?

How about travel on the surface of the earth...

I just want to know, as a first step, whether we are saying that the universe is finite or infinite.

This has been answered several times in this thread by different people.

..whether BBT is compatible with an infinite universe. My reading is that it is not.

A big bang IS compatible...but it is also compatible with a finite one.

The size of the Universe is unknown; it may be infinite.

http://en.wikipedia.org/wiki/Size_of_the_universe#Size.2C_age.2C_contents.2C_structure.2C_and_laws

There are probably more than 100 billion (1011) galaxies in the observable Universe.

That's a LOT of 'different places appearing similar to one another'...meaning coming across a LOT of galaxies, not that each looks exactly the same...

 

[marcus]

My question: Does the cosmological principle imply that the universe is infinite?
...
...

Wiki clearly states: "The cosmological principle implies that at a sufficiently large scale, the universe is homogeneous; different places will appear similar to one another."

Well then, in whichever direction and however far I travel, I will see more of the same. What’s the difference between that and infinity?

...

Big difference!

It is the easiest thing in the world for a spatially finite universe to satisfy homogeneity. To make it simple imagine that space is one-dimensional, with one dimensional galaxies, and the 1D creatures find that if they travel long enough and far enough in one of the two possible directions they find themselves back where they started.
(They discover they live in a finite 1D space with "ring" geometry.)

And then think of the analogous thing in 2D. Space is 2D with 2D galaxies scattered about, and the 2D creatures discover (by exploring and measuring triangles and stuff) that they live in a finite "balloon surface" geometry.

You can't take geometry for granted, you can't assume it is standard Greek Euclidean, you have to find out empirically, by measuring, what the geometry you live in really is. Cosmology is the business of finding out the largescale geometry. Just like the 1D and 2D creatures had to do in the examples.

Now think of the analogous thing in 3D. Imagine space is 3D with 3D galaxies scattered about more or less homogeneously. And suppose we 3D creatures start measuring very large scale triangles to find if there is a very slight deviation from 180 degrees. If there is a consistent pattern of getting very slightly MORE than 180, this will indicate that we live in a finite 3D analog of the "balloon surface" geometry.

So far the measurements have not been conclusive but there are some recent measurements that lean in the direction of that kind of spatial finiteness.

Maybe you should click on the "balloon" link I keep in my signature, and watch the movie a few times. Think about the experience of being in one of those 2D galaxies you see in the movie, with the other galaxies receding from it. finite volume, but no boundary anywhere.

 

[Johninch]

Big difference!

It is the easiest thing in the world for a spatially finite universe to satisfy homogeneity...
Maybe you should click on the "balloon" link I keep in my signature

I did and I also read the rest of Ned Wright's tutorial. The animated sphere has a boundary, so it doesn't help.

You have to see that these pictorial illustrations are doomed to failure, because you can't draw a finite universe without boundaries. It's impossible - you may come to the edge of the paper or let the ink fade out, or draw anykind of complex geometrical shape but you can't demonstrate absence of a boundary with an illustration. And if it can't be shown on paper, this is an indication of the problem.

The oft repeated analogy of the balloon's surface is not translatable to 3D in my mind.

I also want to emphasize that I came off the idea of a crossable boundary some time back. I hope I made it clear that I am only imagining lack of galaxies and other observables from a vantage point within the universe. The problem of the word boundary is that it implies something on the other side and that is not what I mean.

In the meantime I have done more searching and have found a couple of very interesting threads in this forum on this very subject in 2006 and 2007. I have the impression that several posters treating the subject of BBT, expansion, finite/infinite universe, boundary, and so on from a logical point of view were not satisfied before those threads were locked.

I thank everybody for their efforts and I will for sure keep my eyes open for further insights into BBT. As far as I am concerned, the thread can be closed. "Locked" is so aggressive!

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[marcus]

I did and I also read the rest of Ned Wright's tutorial. The animated sphere has a boundary, so it doesn't help.
...

The point of the animated sphere analogy is that it has no boundary. All existence is concentrated on the 2D edgeless surface. The 2D creatures living there cannot point their fingers in any direction that is not on the sphere.
There is no "inside" or "outside" to the sphere.
You have to concentrate in order to get the help from the analogy.

You as a 3D creature cannot point your finger in a 4th spatial direction. In fact we may live in a 3D analog of the 2D sphere. But so far we have no evidence of any "inside" or "outside" or any boundary. No more would 2D creatures living in a universe in which all of existence was concentrated on that animated sphere.

About locking this thread, I am not a moderator or mentor, so I don't decide about those things. Personally I see no reason to lock. If you are dissatisfied or bored you can always drop out. But at this point it's possible someone else might be reading and have questions or comments they want to make. I'm happy with the thread so I think I will hang around a while longer, and see.

Plus you might conceivably change your mind and want to discuss some more. Who knows?

 

[Naty1]

Johnich

...I came off the idea of a crossable boundary some time back... I am only imagining lack of galaxies and other observables from a vantage point within the universe...

Well one CAN imagine being able to look out waaaaaay beyond the current 46bly sphere from which we receive the most distant light. why not...if Einstein could imagine catching up to light we can imagine an 'empty' portion of the universe...

I think I already posted about the fact that each day we receive new CMBR...and it's like yesterdays. No surprises there. Each additional bit looks like the prior homogeneity with small fluctuations...

There may in fact be a 'lack of galaxies' out, say 100 times or 1,000 or 10,000 times further than we can observe today. Nobody can prove that one way or another. But then you should have some reason for such a hypothesis. I can't think of any, we have no such model, but such things don't make it impossible.

It's fun to speculate, to do thought experiments, and then see if they 'pan out' or not. Or whether you can even justify a thought one way or another. The great Richard Feynman noted something to the effect that 'a successful physicist succeeds by making just about every imaginable mistake before arriving at a correct solution.' [I don't mind being shown to be wrong here; I am used to it because my wife does it every day!]

 

[Mordred]

I don't think anyone has a wife that doesn'l lol. Trying to describe outside the universe is like trying to describe non existence. As many are pointing out.

 

[Naty1]

In my next life I'd like to be right all the time...like my wife in this life!

 

[Johninch]

Well one CAN imagine being able to look out waaaaaay beyond the current 46bly sphere from which we receive the most distant light. why not...if Einstein could imagine catching up to light we can imagine an 'empty' portion of the universe.

It is generally accepted that the universe probably extends far beyond the 46 bly observable portion. I do not imagine being able to “look beyond” it, as you suggested, because that is impossible by definition.

I imagine being physically beyond it in another observable portion.

I wasn’t aware that it’s possible to catch up to light – please explain how “Einstein imagined catching up to light”.

I also don’t know what you mean by “an empty portion of the universe”. Do you mean a bubble? A bubble as large as our observable portion would offend the cosmological principle and wouldn’t be compatible with the CMBR measurements as far as I know.

If you mean an empty portion adjacent to a boundary, I don’t think this makes sense. On the one hand it would be merely changing the shape, i.e. ‘drawing in’ the boundary. On the other hand I am doubtful that there could be an empty portion at all. As far as I know, in modern cosmological theory there is no such thing as empty space. Please explain how “we can imagine an empty portion of the universe”.

To repeat, and I hope that I don’t have to repeat this again, my thought experiment was standing at a point in the universe, a long way outside of our observable portion. I look at the sky with the best instruments possible. In a big portion of the sky, say half of it, there is nothing to be observed. I would conclude that there is nothing in that direction and that the universe does not extend any farther in that direction.

There may in fact be a 'lack of galaxies' out, say 100 times or 1,000 or 10,000 times further than we can observe today. Nobody can prove that one way or another. But then you should have some reason for such a hypothesis.

It is not a hypothesis, it’s a question related to the geometry of the universe and whether it can be infinite or not. Marcus has given me good feedback, which you applauded, and I need to digest it, as he suggested. At the moment I am still stuck on the idea of a finite universe with a size and I still don’t accept an infinite one.

Trying to describe outside the universe is like trying to describe non existence. As many are pointing out.

Mordred: I think it is silly to try to describe outside the universe and/ or non-existence. So please don’t attribute these ideas to me.

.

 

[Naty1]

It is generally accepted that the universe probably extends far beyond the 46 bly observable portion. I do not imagine being able to “look beyond” it, as you suggested, because that is impossible by definition.

Ah, but you can in fact see further each time you look!

Next year you will be able to see 'one additional light year' distant...
That's not an actual number but an illustration...But you can do calculations
using the Jorrie on line calculator and figure out such things for yourself...in fact just read Marcus' posts...he has already done many illustrative calculations.

check out the last few pages here for examples:

Look 88 billion years into future and see cosmic event horizon shaping up
https://www.physicsforums.com/showthread.php?t=634757&page=3

please explain how “Einstein imagined catching up to light”.

This was supposedly a 'thought experiment' when Einstein was a teenager...from it, he began his later work on special relativity...refuting the then popular 'aether' theory and instead taking as a given that the speed of light is the same for all intertial observer frames.

 

[Mordred]

No problem just wanted to make sure that all the comments on outside observation were merely a thought experiment.

 

[Johninch]

Ah, but you can in fact see further each time you look!

HaHa! Better than your wife joke!

.

 

[Naty1]

No joke.

You should READ the link so you understand.